Background: We present a novel and systematic approach to analyze temporal microarray data. The approach includes normalization, clustering and network analysis of genes.

Methodology: Genes are normalized using an error model based uniform normalization method aimed at identifying and estimating the sources of variations. The model minimizes the correlation among error terms across replicates. The normalized gene expressions are then clustered in terms of their power spectrum density. The method of complex Granger causality is introduced to reveal interactions between sets of genes. Complex Granger causality along with partial Granger causality is applied in both time and frequency domains to selected as well as all the genes to reveal the interesting networks of interactions. The approach is successfully applied to Arabidopsis leaf microarray data generated from 31,000 genes observed over 22 time points over 22 days. Three circuits: a circadian gene circuit, an ethylene circuit and a new global circuit showing a hierarchical structure to determine the initiators of leaf senescence are analyzed in detail.

Conclusions: We use a totally data-driven approach to form biological hypothesis. Clustering using the power-spectrum analysis helps us identify genes of potential interest. Their dynamics can be captured accurately in the time and frequency domain using the methods of complex and partial Granger causality. With the rise in availability of temporal microarray data, such methods can be useful tools in uncovering the hidden biological interactions. We show our method in a step by step manner with help of toy models as well as a real biological dataset. We also analyse three distinct gene circuits of potential interest to Arabidopsis researchers.

pone-0005098-g002: Correlation matrix before and after uniform normalization.For x = 1, 2, ··· , 16 is the correlation matrix before applying the uniform normalization (see Text S1). For x = 21, 22, ··· , 36 is the correlation matrix after applying the uniform normalization (see Text S1). The diagonal elements of two matrices are all set to 0.

Mentions:
The correlation matrix of 16 replicates of the normalized data as mentioned in Method section and Text S1 is shown in Figure 2. The result obtained after removing the different biases is shown in x ∈ [1], [16]×y ∈ [1], [16]. The existence of negative correlation among the replicates can be seen in Figure 2 (more downward spikes than upward). After applying our method to the data, the negative correlation is evenly distributed over all replicates x ∈ [21, 36]×y ∈ [1,16]. This considerably improves the outcome of the normalization. For a detailed description of the method we refer the reader to the Text S1.

pone-0005098-g002: Correlation matrix before and after uniform normalization.For x = 1, 2, ··· , 16 is the correlation matrix before applying the uniform normalization (see Text S1). For x = 21, 22, ··· , 36 is the correlation matrix after applying the uniform normalization (see Text S1). The diagonal elements of two matrices are all set to 0.

Mentions:
The correlation matrix of 16 replicates of the normalized data as mentioned in Method section and Text S1 is shown in Figure 2. The result obtained after removing the different biases is shown in x ∈ [1], [16]×y ∈ [1], [16]. The existence of negative correlation among the replicates can be seen in Figure 2 (more downward spikes than upward). After applying our method to the data, the negative correlation is evenly distributed over all replicates x ∈ [21, 36]×y ∈ [1,16]. This considerably improves the outcome of the normalization. For a detailed description of the method we refer the reader to the Text S1.

Bottom Line:
The approach is successfully applied to Arabidopsis leaf microarray data generated from 31,000 genes observed over 22 time points over 22 days.Clustering using the power-spectrum analysis helps us identify genes of potential interest.We also analyse three distinct gene circuits of potential interest to Arabidopsis researchers.

Background: We present a novel and systematic approach to analyze temporal microarray data. The approach includes normalization, clustering and network analysis of genes.

Methodology: Genes are normalized using an error model based uniform normalization method aimed at identifying and estimating the sources of variations. The model minimizes the correlation among error terms across replicates. The normalized gene expressions are then clustered in terms of their power spectrum density. The method of complex Granger causality is introduced to reveal interactions between sets of genes. Complex Granger causality along with partial Granger causality is applied in both time and frequency domains to selected as well as all the genes to reveal the interesting networks of interactions. The approach is successfully applied to Arabidopsis leaf microarray data generated from 31,000 genes observed over 22 time points over 22 days. Three circuits: a circadian gene circuit, an ethylene circuit and a new global circuit showing a hierarchical structure to determine the initiators of leaf senescence are analyzed in detail.

Conclusions: We use a totally data-driven approach to form biological hypothesis. Clustering using the power-spectrum analysis helps us identify genes of potential interest. Their dynamics can be captured accurately in the time and frequency domain using the methods of complex and partial Granger causality. With the rise in availability of temporal microarray data, such methods can be useful tools in uncovering the hidden biological interactions. We show our method in a step by step manner with help of toy models as well as a real biological dataset. We also analyse three distinct gene circuits of potential interest to Arabidopsis researchers.